Effect of price changes on the amount spent by consumers and revenue raised by firms, shown both in a diagram and as a calculation

Published by Patrick Mutisya · 14 days ago

IGCSE Economics 0455 – Allocation of Resources: Price Elasticity of Demand (PED)

Price Elasticity of Demand (PED)

1. Definition

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price.

2. Formula

The elasticity coefficient is calculated as:

\$\text{PED} = \frac{\%\;\text{change in quantity demanded}}{\%\;\text{change in price}} = \frac{\Delta Q / Q}{\Delta P / P}\$

3. Interpretation of the coefficient

  • Elastic demand (|PED| > 1) – quantity demanded changes proportionally more than price.

  • Unit‑elastic demand (|PED| = 1) – quantity demanded changes in the same proportion as price.

  • Inelastic demand (|PED| < 1) – quantity demanded changes proportionally less than price.

4. Effect of a price change on consumer spending (total expenditure) and firm revenue

Consumer spending on a good (or a firm’s total revenue) is the product of price (P) and quantity sold (Q):

\$\text{Total Expenditure (Revenue)} = P \times Q\$

Whether a price rise or fall increases or decreases this total depends on the elasticity of demand.

4.1. Elastic demand (|PED| > 1)

If price falls, the increase in quantity demanded is proportionally larger, so total expenditure rises. Conversely, a price rise reduces total expenditure.

4.2. Inelastic demand (|PED| < 1)

If price rises, the decrease in quantity demanded is proportionally smaller, so total expenditure rises. A price fall reduces total expenditure.

4.3. Unit‑elastic demand (|PED| = 1)

Any price change leaves total expenditure unchanged because the percentage change in quantity exactly offsets the percentage change in price.

5. Numerical illustration

Demand typeInitial price (P₀)Initial quantity (Q₀)New price (P₁)New quantity (Q₁)Change in revenueInterpretation
Elastic (|PED| = 2)$10100 units$8150 unitsIncrease ( \$8×150 = \$1,200 > \$10×100 = \$1,000 )Price fall raises total expenditure.
Inelastic (|PED| = 0.5)$10100 units$1290 unitsIncrease ( \$12×90 = \$1,080 > \$10×100 = \$1,000 )Price rise raises total expenditure.
Unit‑elastic (|PED| = 1)$10100 units$1283.33 unitsNo change ( \$12×83.33 ≈ \$1,000 )Revenue unchanged.

6. Diagrammatic representation

A demand curve with three sections (elastic, unit‑elastic, inelastic) can illustrate how total revenue changes when price moves from P₀ to P₁.

Suggested diagram: A single downward‑sloping demand curve labelled with three regions (elastic, unit‑elastic, inelastic). Show two price points (P₀ and P₁) and the corresponding quantities (Q₀ and Q₁). Include rectangles representing total revenue before and after the price change for each region.

7. Summary checklist for exam questions

  1. Identify the elasticity of the good (elastic, unit‑elastic, inelastic).

  2. State the direction of the price change (rise or fall).

  3. Apply the rule:

    • Elastic – price fall → revenue rises; price rise → revenue falls.

    • Inelastic – price rise → revenue rises; price fall → revenue falls.

    • Unit‑elastic – revenue unchanged.

  4. Show the calculation using \$ \text{Revenue}=P\times Q \$ to confirm the conclusion.

  5. Sketch the appropriate portion of the demand curve and label the revenue rectangles.